Lapis Lazuli | Level 10

## Stationarity Test with ADF Test vs Correlation Analysis

Hi I have a time series, which i check it for stationarity using ADF test and arima proc

proc arima data=&td19;
run;
quit;

Below is the ADF test and trend & correlation analysis

i started from the table from the bottom (trend model) and using the Tau compared it with 5% until to reject the null. i concluded that the series is stationary since 0.0315<0.05 zero mean model

However, when i see the ACF/PACF, based on my understanding, the series in not stationary. This is because the ACF decays slowly

My questions are : is this series stationary or not?

 Augmented Dickey-Fuller Unit Root Tests Type Lags Rho Pr < Rho Tau Pr < Tau F Pr > F Zero Mean 0 -2.7655 0.2517 -2.46 0.014 1 -5.0099 0.1214 -2.26 0.0237 2 -3.982 0.168 -2.21 0.027 3 -5.0286 0.1207 -2.27 0.0228 4 -4.2696 0.1532 -2.14 0.0315 Single Mean 0 -2.5618 0.7064 -1.71 0.4237 3.03 0.2995 1 -6.4379 0.3047 -2.17 0.2186 2.78 0.3619 2 -4.6272 0.4645 -1.92 0.3218 2.49 0.437 3 -6.5225 0.2983 -2.17 0.2192 2.8 0.3657 4 -5.2232 0.4056 -1.93 0.315 2.39 0.4685 Trend 0 -3.4578 0.9132 -1.23 0.8994 1.52 0.8742 1 -16.6892 0.1154 -2.83 0.1917 4.32 0.3133 2 -10.7554 0.3659 -2.18 0.4973 2.8 0.6186 3 -19.6884 0.0597 -2.79 0.2033 4.29 0.3316 4 -15.4981 0.1473 -2.39 0.3834 3.22 0.5402

2 REPLIES 2
Super User

## Re: ADF Test vs Correlation Analysis

the series in not stationary.

Maybe You need create a new variable = interest_rate - lag4(interest_rate) .
and use this new variable to run ADF ,and check if it is stationary .
Lapis Lazuli | Level 10

## Re: ADF Test vs Correlation Analysis

hi, thanks for your response. I have created the new variable :

newvar = interest_rate - lag4(interest_rate);

and run again the arima proc, below you can see the results

The table shows that the Tau = 0.0045 < 0.05 which means that it is stationary. The ACF decays faster but PACT has 1st lag significant

What is the conclusion? Does the below mean that the variable interest_rate is not stationary ?

 Augmented Dickey-Fuller Unit Root Tests Type Lags Rho Pr < Rho Tau Pr < Tau F Pr > F Zero Mean 0 -10.5703 0.022 -2.35 0.0188 1 -57.9428 <.0001 -5.44 <.0001 2 -47.1978 <.0001 -4.35 <.0001 3 -49.3153 <.0001 -4.28 <.0001 4 -24.2331 0.0003 -3.01 0.003 Single Mean 0 -11.2029 0.092 -2.41 0.1419 2.9 0.3406 1 -62.2964 0.0009 -5.57 <.0001 15.55 0.001 2 -52.644 0.0009 -4.49 0.0005 10.07 0.001 3 -55.7943 0.0009 -4.35 0.0007 9.55 0.001 4 -27.2889 0.0011 -3.07 0.0327 4.74 0.049 Trend 0 -11.7463 0.3063 -2.48 0.3379 3.09 0.5647 1 -64.2625 0.0003 -5.62 <.0001 15.8 0.001 2 -55.4468 0.0003 -4.55 0.0022 10.33 0.001 3 -57.8565 0.0003 -4.32 0.0045 9.46 0.001 4 -28.5013 0.007 -3.07 0.1194 4.74 0.2431

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